Bounds for the Isothermal, Adiabatic, and Isolated Static Susceptibility Tensors

Abstract

Quantum-statistical proofs are given that the isolated (or Kubo) susceptibility tensor is positive indefinite and is bounded from above by the adiabatic susceptibility tensor, while the isothermal susceptibility tensor is positive definite and is bounded from below by the adiabatic susceptibility tensor. The results apply to either the static dielectric or magnetic cases. Biasing fields and permanent dipole moments may be present if desired. Criteria for equality of the various susceptibilities are established. Contact is made with work of Falk, Caspers, Mountain, Klein, Rosenfeld, and Saito.

Nonperturbative landscape of the Mott-Hubbard transition: Multiple divergence lines around the critical endpoint

“…As a consequence, at the two-particle level specific differences emerge between the two models due to the intrinsic differences in the nature of the disorder: Specifically, the isothermal response of the systems, and hence its static susceptibility (Ω = 0), differs 59 due the absence/presence of a thermal-ensemble averaging of the scattering potential in the BM/FK (quenched/annealed disorder), respectively. In spite of this difference, we will demonstrate that the specific vertex anomalies found in the BM at Ω = 0 can be also observed in the FK model.…”

Minimal work principle: Proof and counterexamples

“…(26,34) as applied to the full cyclic process (i.e., changing in them t f → t ′ f ), Eq. (70) implies:…”

“…• Only two features of the initial state ρ(t i ) were used: [H i , ρ(t i )] = 0 determined the specific form (26,27) of the work, while Eq. (23) was used in proving Θ m ≥ 0 in Eq.…”

“…Concrete estimates for the rate of convergence were given. iii) It was found that for certain non-trivial macroscopic systems the above convergence can be absent even in the thermodynamical limit [24,26]. It was argued that quantum systems are more vulnerable in this respect than classical ones [24].…”

On the spectral relations for multitime correlation functions

“…But very soon it was noticed that spectral relations should be completed by a special treatment of the pole at zero frequency, which gives additional contribution connected with the presence of the conserving quantities [5][6][7]. Later, it was shown that such contributions describe the difference between the isothermal and isolated response of the many-body system and are specific for the non-ergodic systems [1,[6][7][8] where the regions exist in the phase space which cannot be achieved by the trajectory of the point that describes an evolution of the many-body system. In the Green's function formalism, the issue of ergodicity appears as a difficulty in determining the zero-frequency bosonic propagators [5][6][7][9][10][11][12][13][14][15][16][17][18].…”